Finite Group Databasebeta

← #34079897

Subgroups — #34079897

Order 19328.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752722C212yesmaximal, complemented
2#23752555C212yesmaximal, complemented
3#23752534C212yesmaximal, complemented
4#23752453C211yesmaximal, characteristic, complemented
5#23752439C212yesmaximal, complemented
6#23752375C212yesmaximal, complemented
7#23752354C212yesmaximal, complemented
8C2×(C2×D151)⋊C8C211yesmaximal, characteristic, complemented
9#466×C151C211yesmaximal, characteristic, complemented
10C2×#14559003C2212yes—
11C22×C4×D151C2211yescharacteristic
12C2×Dic604C2211yescharacteristic, complemented
13C2×#14558992C2212yescomplemented
14C22×C151⋊C8C2211yescharacteristic
15#18012721—22no—
16#18012719C2212yes—
17#18012718C2212yes—
18#18012710C2212yes—
19#18012707—22no—
20D4×Dic151—22no—
21(C22⋊D151)⋊C4—22no—
22#18012697C2212yes—
23#18012673C2211yescharacteristic, complemented
24#18012670C2212yescomplemented
25#18012664C2212yescomplemented
26#18012662C2212yescomplemented
27#18012660C2212yescomplemented
28(C2×D151)⋊C8C2212yes—
29(C2×D151)⋊C8C2212yes—
30C2×D8×C151C2211yescharacteristic, complemented
31C22×C8×C151C2211yescharacteristic
32#121×C151C2212yes—
33#107×C151C2211yescharacteristic, complemented
34#102×C151C2212yescomplemented
35C23×D151D411yescharacteristic
36#14559003—42no—
37#14559003—42no—
38C2×Dic302C2312yes—
39C2×C22⋊D151—22no—
40C2×C22⋊D151—22no—
41C22×Dic151—22no—
42C22×Dic151D411yescharacteristic
43C2×C4×D151—41no—
44C2×C4×D151—41no—
45C2×C4×D151D412yes—
46C2×C4×D151C2312yes—
47Dic604—41no—
48#14558992—42no—
49C2×C151⋊C8—41no—
50C2×C151⋊C8C2312yes—
51C4⋊Dic151—22no—
52C4⋊Dic151C2312yes—
53Dic151⋊C4—22no—
54C22⋊Dic151—22no—
55C22⋊Dic151—22no—
56(C2×D151)⋊C4—22no—
57(C2×D151)⋊C4—22no—
58C4×Dic151—22no—
59C2×D4×C151—22no—
60C2×D4×C151C2312yes—
61C22×C4×C151C2311yescharacteristic
62D8×C151—41no—
63C2×C8×C151—41no—
64C2×C8×C151C2311yescharacteristic
65C2×C8×C151C2311yescharacteristic
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C22×D151—22no—
69C22×D151—41no—
70C22×D151—41no—
71C22×D151C2×D412yes—
72Dic302—22no—
73Dic302—22no—
74C22⋊D151—44no—
75C22⋊D151—44no—
76C2×Dic151—22no—
77C2×Dic151—22no—
78C2×Dic151—41no—
79C2×Dic151—44no—
80C2×Dic151C2×D412yes—
81C4×D151—22no—
82C4×D151—22no—
83C4×D151—42no—
84C151⋊C8—22no—
85C23×C151—22no—
86C23×C151C2×D411yescharacteristic
87D4×C151—22no—
88D4×C151—22no—
89D4×C151—44no—
90C2×C4×C151—21no—
91C2×C4×C151—21no—
92C2×C4×C151—22no—
93C2×C4×C151C2×D411yescharacteristic
94C2×C4×C151C2411yescharacteristic
95C8×C151—21no—
96C8×C151—21no—
97C22×C151—21no—
98C22×C151—21no—
99C22×C151—42no—
100C22×C151—42no—
101C22×C151—42no—
102C22×C151#13512yes—
103C22×C151C22×D411yescharacteristic
104C2×D151—22no—
105C2×D151—22no—
106C2×D151—22no—
107C2×D151—44no—
108C4×C151—21no—
109C4×C151—42no—
110C4×C151H(5,𝔽2)11yescharacteristic
111C4×C151H(5,𝔽2)11yescharacteristic
112Dic151—22no—
113Dic151—42no—
114Dic151—42no—
115C2×C151—22no—
116C2×C151—82no—
117C2×C151#53411yescharacteristic
118C2×C151C2×#13511yescharacteristic
119C2×C151#57511yescharacteristic
120D151—42no—
121C151#319111yescharacteristic, complemented, Sylow
122#3191—1511nomaximal, Sylow
123#525—1512no—
124#485—1512no—
125#482—1512no—
126#467—1511no—
127#466D15111yescharacteristic, complemented
128#465—1512no—
129#452—1512no—
130#449—1512no—
131C2×C22⋊C8—1511no—
132C2×#41—1512no—
133C23×C4—1511no—
134C2×Q16—1511no—
135C2×SD16—1512no—
136C2×D8C2×D15111yescharacteristic, complemented
137C22×C8—1511no—
138C22×C8C2×D15111yescharacteristic
139#123—3022no—
140C22⋊Q8—1512no—
141C22⋊Q8—1512no—
142#121—1512no—
143#121C2×D15112yes—
144#120—3022no—
145C4×D4—3022no—
146C4×D4—3022no—
147#117—1512no—
148#107—1511no—
149#107C2×D15111yescharacteristic, complemented
150#106—1512no—
151#103—1512no—
152#103—1512no—
153#102—1512no—
154#102C2×D15112yescomplemented
155C22⋊C8—1512no—
156C22⋊C8—1512no—
157C24—1511no—
158#41—6042no—
159#41—6042no—
160C2×Q8—1512no—
161C2×D4—22no—
162C2×D4—3022no—
163C2×D4—3022no—
164C2×D4C22×D15112yes—
165C22×C4—3022no—
166C22×C4—6041no—
167C22×C4—6041no—
168C22×C4—1512no—
169C22×C4—1511no—
170C22×C4—1512no—
171C22×C4C22×D15111yescharacteristic
172Q16—6041no—
173SD16—6042no—
174D8—41no—
175C2×C8—41no—
176C2×C8—6041no—
177C2×C8—1512no—
178C2×C8C22×D15111yescharacteristic
179C2×C8C22×D15111yescharacteristic
180C4⋊C4—3022no—
181C4⋊C4—3022no—
182C4⋊C4—1512no—
183C4⋊C4C22×D15112yes—
184C22⋊C4—22no—
185C22⋊C4—3022no—
186C22⋊C4—3022no—
187C22⋊C4—3022no—
188C22⋊C4—3022no—
189C42—3022no—
190C23—22no—
191C23—3022no—
192C23—6041no—
193C23—6041no—
194C23—1512no—
195C23D4×D15111yescharacteristic
196Q8—3022no—
197Q8—3022no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—6044no—
202D4—6044no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—3022no—
207C2×C4—3022no—
208C2×C4—3022no—
209C2×C4—3022no—
210C2×C4—6042no—
211C2×C4—6041no—
212C2×C4—6044no—
213C2×C4—1512no—
214C2×C4D4×D15111yescharacteristic
215C2×C4C23×D15111yescharacteristic
216C8—21no—
217C8—21no—
218C8—3022no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—3022no—
225C22—3022no—
226C22—3022no—
227C22—6044no—
228C22#1801275812yes—
229C22C2×D4×D15111yescharacteristic
230C4—21no—
231C4—42no—
232C4—3022no—
233C4—6042no—
234C4—6042no—
235C4#1801278411yescharacteristic
236C4#1801278511yescharacteristic
237C2—22no—
238C2—82no—
239C2—6042no—
240C2#2375277011yescharacteristic
241C2C2×#1801275811yescharacteristic
242C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#466×C151C2
socleC22×C151C22×D4
hypercenter#466D151
hypocenterC151#3191
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23752722C2semidirect
2. #23752555C2semidirect
3. #23752534C2semidirect
4. #23752453C2semidirect
5. #23752439C2semidirect
6. #23752375C2semidirect
7. #23752354C2semidirect
8. C2×(C2×D151)⋊C8C2semidirect
9. #466×C151C2semidirect
12. C2×Dic604C22semidirect
13. C2×#14558992C22semidirect
23. #18012673C22semidirect
24. #18012670C22semidirect
25. #18012664C22semidirect
26. #18012662C22semidirect
27. #18012660C22semidirect
30. C2×D8×C151C22semidirect
33. #107×C151C22semidirect
34. #102×C151C22semidirect
121. C151#3191semidirect
127. #466D151semidirect
136. C2×D8C2×D151semidirect
149. #107C2×D151semidirect
154. #102C2×D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237527222
#237525552
#237525342
#237524532
#237524392
#237523752
#237523542
C2×(C2×D151)⋊C82
#466×C1512
#3191151